Power Scaling on Efficient Generation of Ultrafast Terahertz Pulses

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008 315

Power Scaling on Efficient Generation of UltrafastTerahertz Pulses

Xiaodong Mu, Ioulia B. Zotova, and Yujie J. Ding, Senior Member, IEEE

Abstract—We have investigated power scaling for the efficientgeneration of the broadband terahertz (THz) pulses. These THzshort pulses are converted from ultrafast laser pulses propagatingin a class of semiconductor electrooptic materials. By measuringthe dependence of the THz output on the pump beam in terms ofincident angle, polarization, azimuthal angle, and pump intensity,we have precisely determined the contributions made by opticalrectification, drift of carriers under a surface or external field,and photo-Dember effect. When a second-order nonlinear mate-rial is pumped below its bandgap, optical rectification is always themechanism for the THz generation. Above the bandgap, however,the three mechanisms mentioned earlier often compete with oneanother, depending on the material characteristics and pump in-tensity. At a sufficiently high pump intensity, optical rectificationusually becomes the dominant mechanism for a second-order non-linear material. Our analysis indicates that second-order nonlinearcoefficients can be resonantly enhanced when a material is pumpedabove its bandgap. In such a case, the THz output power and nor-malized conversion efficiency can be dramatically increased. Wehave also analyzed how the THz generation is affected by somecompeting processes such as two-photon absorption.

Index Terms—Broadband THz pulses, difference-frequencygeneration (DFG), drift of carriers under electric field, electroop-tic materials, optical rectification, photo-Dember effect, quasi-single-cycle THz pulses, resonant second-order nonlinearities, two-photon absorption (2PA).

I. INTRODUCTION

T ERAHERTZ (THz) domain in the electromagnetic spec-trum offers certain advantages compared with the rest of

the frequency regions. For example, since the transition fre-quencies between rotational states in certain gases are withinthis region [1], fingerprinting the corresponding molecules isfeasible in the THz region [2]. Furthermore, THz is capable oftaking phase-sensitive images containing spectroscopic infor-mation [3]. In almost all the applications for THz waves, highoutput powers for the THz pulses are necessary in order to fullyutilize their capabilities. In the case of chemical sensing, e.g, ahigh-power THz beam can interact with the chemical speciesfor multiple round trips, and therefore, the detectability of thechemical species can be significantly improved. On the otherhand, for the THz imaging through atmosphere, higher outputpowers for the THz beam would allow us to take an image froman object farther away. However, in the past, since the output

Manuscript received September 30, 2007. This work was supported by theU.S. Air Force Office of Scientific Research and Air Force Research Laboatory.

X. Mu and Y. J. Ding are with the Department of Electrical and ComputerEngineering, Center for Optical Technologies, Lehigh University, Bethlehem,PA 18015 USA (e-mail: [email protected]; [email protected]).

I. B. Zotova is with ArkLight, Center Valley, PA 18034 USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/JSTQE.2007.913961

powers for the broadband THz pulses are relatively low, theapplications of the broadband THz pulses have not been fullyexploited.

As the output powers of the THz sources are improved, onewill be able to directly measure the spectrum of the reflectedand transmitted THz signals by using the detectors operatingat room temperature. Among different types of the THz detec-tors, a bolometer has a typical noise-equivalent power (NEP) of100 fW/

√Hz.1 However, such a NEP value is achievable only

at the liquid-helium temperature. Beside bolometers, pyroelec-tric detectors based on deuterated L-alanine triglycine sulphate(DLATGS) can have a NEP value as low as 10 nW/

√Hz.1

Therefore, for the output power of the THz pulses to be 1 µW, apower attenuation by 13 dB (a factor of 18) can be still detectedby using such a detector operating at 30 Hz. Such attenuationallows us to utilize the atmospheric window near 850 GHz forreaching an imaging distance of >50 m [4]. If the THz outputpower is increased to 1 W, a detectable attenuation of 73 dBis feasible, which corresponds to a distance of 360 m. Anothertype of the detectors working at room temperature is a Keatingpower meter. However, such a detector has a much higher NEPvalue, i.e., 2 µW/

√Hz,1 which is translated into a measurable

THz power of about 11 µW at 30 Hz. Obviously, scaling up theoutput powers to much higher values is necessary in order toutilize such a detector to implement the applications describedearlier.

On the other hand, THz time-domain spectroscopy [3] hasbecome a quite sensitive technique for detecting the coherentlygenerated THz pulses. Via such a scheme, only a relativelylow THz power (i.e., ∼100 nW) is required [5]. However, sucha technique may not be applicable when the phase coherencebetween the optical pump and detected THz pulses cannot bemaintained. With relatively high THz intensities available, onewould be able to explore a nonlinear regime of the interactionsbetween the intense THz pulses and a variety of the nonlinearmedia covering from chemical vapors [6] to amorphous andcrystalline solids [7].

In the past, three schemes have been investigated for produc-ing broadband THz pulses: optical rectifications [i.e., difference-frequency generation (DFG) within each pulse] [8], [9], pho-toconduction [10], and Cherenkov radiation [11], [12]. Theseschemes all require ultrafast laser pulses to pump electroopticmaterials. So far, the record-high output peak power is perhaps5.0 MW with the corresponding power conversion efficiency0.062% [13]. However, in order to reach such a high output peakpower, the peak pump power is required to be 40 GW. As a result,

1These values are taken from our measurements.

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316 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 2, MARCH/APRIL 2008

the conversion efficiency normalized by the peak pump poweris determined to be 0.0015%/GW. In addition, since the repeti-tion rate is 10 Hz, the average THz output power is limited to100 µW. Furthermore, the central frequency of the THz output isrelatively low and its pulse is rather broad. It is worth noting thatthere are a variety of the configurations for further enhancingthe conversion efficiencies from the optical to THz pulses. Someof the examples include the incorporations of photonic crystalmicrocavities [14], waveguides [15], and intracavity DFG [16].

In this article, we summarize our results on power scalingof the broadband THz pulses generated by using ultrafast laserpulses propagating in a class of semiconductor electrooptic ma-terials. Our approach is to maximize the normalized conversionefficiency for the broadband THz pulses while keeping the av-erage output powers as high as possible. As one can see later,such an optimization allows us to use a pump laser with a rel-atively low energy per pulse and a quite high repetition rate. Insuch a case, we can minimize some competing nonlinear pro-cesses that could deteriorate the electrooptic material used forthe THz conversion [17]. It is worth noting that the requirementon a THz source depends on the type of the application. Forexample, in order to investigate a nonlinear interaction betweenintense THz pulses and a medium with a rather fine temporalresolution, subpicosecond THz pulses with very high outputpeak powers are required. In such a case, it is important for aresearcher to use a THz source generating quasi-single-cyclepulses in order to avoid the effects caused by the damped oscil-lations superimposed with the dominating THz pulses [17]. Onthe other hand, for THz imaging high average output powers forthe THz source are preferred. For the applications in chemicaldetections, a THz source with a rather broad bandwidth and areasonably high repetition rate should be the choice.

This paper is organized as follows. In Section II, we briefly re-view our theory on the THz generation based on optical rectifica-tion. In Section III, we summarize our results on the nonresonantTHz generation, i.e., each electrooptic material is pumped belowits bandgap. Under such a case, optical rectification is alwaysthe primary mechanism for the THz generation. In Section IV,we discuss our results on the THz generation for the pump beamabove the bandgap of each electrooptic material. As one can seelater, in this case, the output powers and conversion efficienciescan be resonantly enhanced. In Section V, we summarize ourresult following our investigation of the THz generation in aSi film on the top of SiO2 , in which the THz radiation exhibitscompletely different features from the nonresonant and resonantTHz generation. Depending on the material characteristics andpump intensity, three mechanisms for the THz generation, i.e.,optical rectification, drift of carriers under an electric field, andphoto-Dember effect, may complete with one another. Finally,in Section VI, we draw concluding remarks. We will make anacknowledgment statement afterwards.

II. THZ GENERATION BASED ON OPTICAL RECTIFICATION:THEORY

In this section, we briefly review our theory on the THzgeneration based on optical rectification.

We have shown [17], [18] that the coherence lengths for theTHz generation based on the DFG within each ultrafast infraredpulse can be sufficiently long for a wide bandwidth around eachphase-matching wavelength due to a slight dispersion in theTHz region. As a result, quasi-single-cycle THz pulses can beefficiently generated. An efficient conversion for the parametricprocess is made possible not only by utilizing the wide phase-matching bandwidth but also by optimizing the pulse widthfor each peak THz frequency. In order to efficiently generatehigh peak intensities for the THz pulses, we have investigatedthe strong pump regime and found the limits to the conversionefficiencies.

Consider an electric field of the ultrafast infrared pulses inthe form of

Ep(r, t) = [ε(r, t)/2] exp[i(ωpt − kp · r)] + c.c. (1)

where ωp and kp = 2πnp/λp are the frequency and wave vectorfor the pump pulses with λp and np the wavelength and indexof refraction, and ε(r, t) is an envelope slowly varying in rand t describing the propagation of each pump pulse [19]. ATHz wave can then be generated as a result of the DFG amongall the pairs of the frequency components within each pumppulse in a second-order nonlinear medium. We assume that z-axis is the propagation direction of the pump and THz wavesand we neglect linear absorption, two-photon absorption (2PA),three-photon absorption (3PA), free-carrier absorption (FCA),nonlinear refractive index (NRI), and all the Fresnel reflections.Taking Fourier transforms (denoted by bars) of the two coupledMaxwell’s equations for the pump and THz waves [20], weobtain the coupled wave equations

[∇2+

Ω2

c2 n2 (Ω)]

ETHz (r,Ω)=2deff

c2

∫ +∞

−∞

(∂2E2

p

∂t2

)e−iΩt dt

= −deff Ω2

c2 |ε|2 (2a)

[i

2kp∇2

t +∂

∂z+ i

npgΩc

+i

2k′′

pΩ2]

ε∼ = −2ideff ωp

cnpETHz ε

∼

(2b)where npg is the group index at λp , k′′

p is the group velocitydispersion (GVD) parameter [19], deff (Ω) is the effective non-linear coefficient of the medium at Ω, and n(Ω) is the index ofrefraction at Ω. In order to find out scaling laws for the THzgeneration, we simply our calculations by assuming that boththe pump and THz waves are the plane waves and GVD is neg-ligible. Consider ε (z, t) = E0g [(t − npg z/c)/τ ], where E0 isthe magnitude of the electric field for the pump wave and τ isthe effective pulse width. Neglecting the pump depletion, onecan simplify (2a) to[

∂2

∂z2 +Ω2

c2 n2 (Ω)]

ETHz (z,Ω)

= −deff E20 Ω2g2 (0,Ω)

c2 e−iΩ n p g z

c . (3)

MU et al.: POWER SCALING ON EFFICIENT GENERATION OF ULTRAFAST TERAHERTZ PULSES 317

Based on ETHz (0,Ω) = 0; ∂ETHz (0,Ω) /∂z = 0, one canthen obtain the solution to (3) [17], [18]:

ETHz (L,Ω) = − ideff E20 Ωg2 (0,Ω) L

c (npg + n)sin c

[Ω2c

(npg − n) L

]

× exp[−i

Ω2c

(npg + n) L

](4)

where L is the length of the nonlinear medium. One cansee from (4) that ETHz (L,Ω) is the product between thespectral and phase-matching terms. For Gaussian pulses, i.e.,g(0, t) = e−t2 /τ 2

, g2(0,Ω) = (√

π/2τ)e−τ 2 Ω2 /8 . On the otherhand, for hyperbolic-secant pulses, i.e., g(0, t) = sech(t/τ),g2(0,Ω) = πΩτ 2/ sinh(πΩτ/2). For such a profile, the spec-tral term has a peak (i.e., central) frequency of ΩTHz ≈ 1.219/τ .In addition, the spectral bandwidth is defined between the twofrequencies, determined at the half of the peak spectral intensity,given by Ωlow ≈ 0.5652/τ ; Ωhigh ≈ 2.147/τ. Furthermore, thephase-matching term reaches the maximum value of 1 when thephase-matching condition is satisfied [17], [18], [21], [22]:

n (ΩTHz) = npg (ωp) (5)

i.e., the THz phase index must match the pump group index.This condition is similar to that for the Cherenkov radiationused for the THz generation [12]. It is worth noting that forthe DFG from the two single pump frequencies [23], (5) isan approximate expression for the phase-matching condition.According to (4) the coherence length for the THz generation isdefined as [17], [18], [21], [22]:

Lc = λ/ (2 |npg − n|) (6)

where λ = 2πc/Ω. If L ≈ Lc within the spectral bandwidthdefined earlier, the phase-matching bandwidth is approximatelyequal to the spectral bandwidth. Consider the condition whenthe phase-matching bandwidth is much wider than the spectralbandwidth defined earlier, which is approximately the same asthe ideal case when (5) is satisfied for every output frequency,see Fig. 1.

To obtain an expression for the instantaneous electric field ofthe THz pulses, one can take Fourier transform of (4):

ETHz (L, t) = − iE20 L

2πc

∫ +∞

−∞

deff Ωg2 (0,Ω)npg + n

× sin c

[Ω2c

(npg−n) L

]

× exp

iΩ[t − L

2c(npg + n)

]d Ω. (7)

According to (7), the ideal case defined earlier is actuallyequivalent to the condition of a sufficiently short nonlinearmedium, i.e., L 4cτ/(nTHzg − npg ), where nTHzg is theTHz group index at ΩTHz . Assuming deff is independent ofΩ, we can then simplify (7) to

ETHz (L, t) = −deff E20 L

2cnpg

∂g2 [(t − npgL/c)/τ ]∂t

(8)

Fig. 1. Normalized spectral electric field amplitude versus normalized fre-quency Ωτ based on (4), for broadband phase-matched DFG or ideal case,i.e., sin c [Ω (npg − n) L/ (2c)] = 1 for any Ω, and hyperbolic-secant pumppulses (solid line). For comparison, normalized spectral electric field amplitudeis also plotted versus normalized frequency for 2-mm-long GaP and ZnGeP2crystals at pump wavelengths of 1.034 and 1.218 µm to produce central outputwavelengths of 550 and 300 µm, respectively, based on (4) for hyperbolic-secant pulses and with the Sellmeier equations given by footnote 2 and [27],corresponding to dotted and dashed lines, respectively.

i.e., the THz electric field is determined by the deriva-tive of the pump intensity with respect to time regard-less of the pulse shape. For the Gaussian pulses, ∂g2/∂t =−

[4 (t − npgL/c)

/τ 2

]e−2[(t−np g L/c)/τ ]2 . On the other hand,

for the hyperbolic-secant pulses

ETHz (L, t) =deff E2

0 L

cnpg τ

tanh [(t − npgL/c)/τ ]cosh2 [(t − npgL/c)/τ ]

(9)

i.e., a perfect single-cycle pulse. Using (1/c) ∂HTHz/∂t =−∂ETHz/∂z, one can obtain the pulse energy density for theTHz wave (JTHz) and then the conversion efficiency

η =JTHz

Jp=

2d2eff L2η0

15c2npgn2pτ

3

(Jp

Ap

)(10)

where Jp and Ap are the pulse energy and focal area of the pumpbeam and η0 is the vacuum impedance. One can see from (10)that the conversion efficiency and THz pulse energy are inverselyproportional to the cubic power of the pump pulse width. SinceΩTHz ≈ 1.219/τ , η ∝ Ω3

THz . Therefore, there is an obviousadvantage of using short pump pulses corresponding to the highcentral THz frequencies. However, only when both the phase-matching condition, (5), is satisfied and the phase-matchingbandwidth is broad enough, one can gain the huge enhancementdue to the spatial accumulation reflected by JTHz , η ∝ L2 in(10). However, when the phase mismatch is sufficiently high andthe pulse width of the pump beam is short enough, multicycleTHz pulses are generated [28].


Based on (10), one can define a normalized conversion effi-ciency given by:

η =ητp

Jp≈ 0.7306η0d

2eff L2Ap

c2n2pτ

2p

(11)

where τp ≈ 1.763τ is the pulse width. The normalized conver-sion efficiency defined earlier can be used to compare amongdifferent materials when the beam radius for the pump iskept as a constant. One can see from (11) that η ∝ L2

/τ 2p

or η ∝ L2Ω2THz . Assuming that the pump beam is focused

down to reach an optimal confocal beam parameter, Ap ≈2πcL/ΩTHznpg . Under such a condition, the divergence of thepump beam within the crystal is negligible. Substituting Ap insuch an expression into (10), one obtains

ηopt ≈0.2499η0d

2eff JpL

c3n2pτ

4p

. (12)

Such an expression can be used to make a simplified calculationwhen the divergence of the THz beam within the crystal is takeninto consideration. Therefore, in such a case ηopt ∝ L

/τ 4p or

ηopt ∝ LΩ4THz , i.e., the scaling laws for the length of the non-

linear medium and central frequency are quite different fromthat based on (10) where Ap is assumed to be independent ofthe crystal length and THz frequency. Under such an optimal fo-cusing condition, we can define another normalized conversionefficiency as

≈η= τpηopt/JpL. For the optimal power scaling

law, this normalized conversion efficiency should be kept as aconstant as the pump power is significantly increased. It is worthnoting that our frequency scaling law based on (12) is differentfrom that for the generation of narrow-band THz packets byusing ultrafast laser pulses [29].

Substituting (9) and ε (L, t) for the hyperbolic-secant pulsesinto the right-hand side of (2b) for the plane waves with k′′

p = 0and taking Fourier transform of the resulting expression, oneobtains

ε (L, t) ≈ E0

cosh [(t − npgL/c) /τ ]

× exp−iη

(15ωpτ

2

)tanh [(t − npgL/c)/τ ]cosh2 [(t − npgL/c)/τ ]

.

(13)

The term inside the braces of (13) defines an effective NRI dueto the cascaded second-order parametric processes [17].

Due to the existence of a reststrahlen band for all electroop-tic materials, we have chosen λp in such a way that within thespectral bandwidth of the THz output wave, the absorption isnegligible. As a result, the central output wavelength determinedby (5), i.e., λTHz , is 300 µm or longer. For a bulk GaP crystal,2

an Yb-doped laser or amplifier at λp ≈ 1.031 µm can be usedas a pump source to produce λTHz ≈ 300 µm. The bandwidthof the output wave is then defined between 170 and 366 µm.

2GaP: the Sellmeier equation is taken from [24]; GaAs: the near-IR Sellmeierequation is taken from [25]; while the THz Sellmeier equation is in the form of√

b1 + b2λ2/(λ2 − b3 ) with the three constants: b1 , b2 , and b3 , given by the

best fit to the data in [26].

The optimal full-width at half maximum (FWHM) pulse widthis τp ≈ 2.149/ΩTHz ≈ 341 fs. The GaP offers an advantagefor the generation of high output powers over other crystalssince its 2PA coefficient is negligible at 1.031 µm. One can seefrom Fig. 1 that the THz pulses generated from a GaP crystalcan be approximated by single cycles (i.e., quasi-single cycles).Consider a peak pump power of 3.3 MW, Ap ≈ 0.22 mm2 ,and L ≈ 2 mm, one can calculate the THz peak intensity to beabout 3.4 × 105 W/cm2 (a peak power of 243 W) based on(10). Such an output power corresponds to η ≈ 8.9 × 10−5 . Atsuch a conversion efficiency, the effective NRI change is about7.5 × 10−6 according to (13) (n2 ≈ 5.0 × 10−15 cm2/W). Fora bulk GaAs crystal with λp ≈ 1.395 µm or 1.374 µm based onthe Sellmeier equations given by footnote 2 and [30], respec-tively, λTHz ≈ 300 µm. Assuming L ≈ 1 cm, an average pumppower of 1 W, a repetition rate of 76 MHz, and Ap ≈ 1.0 mm2 ,one obtains η ≈ 2.2 × 10−5 (average output power of 22 µW)based on (10). On the other hand, for a ZnGeP2 crystal at λp ≈1.218 µm, λTHz ≈ 300 µm by using the Sellmeier equations[27]. According to Fig. 1, the output pulses have the character-istics of quasi-single cycles.

It is worth noting that when the phase-matching condition,(5), cannot be satisfied, the crystal length in (10)–(12) shouldbe replaced by the coherence length for the THz generation Lc ,given by (6). If the efficient absorption length for the pumpand THz waves (Lα ) is shorter than Lc , L in (10)–(12) shouldbe then replaced by Lα . If Lα is comparable to Lc , there isan optimum crystal length [31]. For the pumping conditionsconsidered earlier, we have estimated the contributions due toGVD, 2PA, 3PA, FCA, and NRI [17], which can all be neglected.In addition, the variations of the relevant physical quantitiessuch as the pump intensities and carrier temperatures along thez-axis have negligible effects on the phase-matching condition.Using a 2-mm-long ZnTe crystal at λp ≈ 810 nm, however, theoutput is a decayed oscillation over many cycles, correspondingto a spectral peak that is much narrower than that shown inFig. 1 [17], [21].

In order to find out the upper limits of the conversion efficien-cies and output powers, we numerically solved (2a) and (2b) forthe plane waves [17]. Consider λp ≈ 1.031 µm in a 2-mm-longGaP crystal (k′′

p = 1.3 fs2/µm). When the peak pump intensityis increased to 38 GW/cm2 , the upper limit to the conversionefficiency is 0.23%, which approaches

∆ωp/ωp ≈ 0.32% (14)

where ∆ωp ≈ 1.122/τ is the pump bandwidth. Therefore, thefraction of the pump bandwidth appears to be the bound valuefor the conversion efficiency. Such a claim is probably validregardless of whether the THz parametric processes can be cas-caded or not. According to our results, the distortions of the THztemporal profiles due to the pump depletion are still negligible,see Fig. 2. However, at the high end of the pump intensities, thespectral and temporal electric fields of the pump beam sufferfrom severe distortions. Furthermore, both 3PA and FCA maycompete with the THz generation. The dispersion of deff couldslightly modify the pulse profiles. As a result, some of these high


Fig. 2. For a 2-mm-long GaP crystal (λp ≈ 1.031 µm and k′′p =

1.3 fs2 /µm), normalized instantaneous electric field versus normalized time(t − npg L/c)/τ for three different pump intensities: 1.5 GW/cm2 , solid line;14 GW/cm2 , dashed line; and 38 GW/cm2 , dotted line.

peak intensities may exceed a damage threshold for a particularGaP crystal. Some of these issues were addressed by us in [17].If the 3PA coefficient and FCA can be reduced, it is possible touse GaP for the efficient THz generation with an output peakpower reaching 150 kW, corresponding to the peak intensity of210 MW/cm2 . One may use a GaP/AlGaP channeled waveg-uide for the THz wave, resulting in a decrease of the THz phaseindex by 0.13 [15], [32], which is sufficient to confine the THzwave such that the pump wavelength shifts to λp ≈ 1.339 µm.At such a pump wavelength, 3PA can be neglected.

III. NONRESONANT THZ GENERATION

In this section, we summarize our results on the THz genera-tion when each of the electrooptic materials considered here ispumped below its bandgap, i.e., nonresonant case.

A. GaP and ZnTe

We first investigate the competition between efficient THzgeneration and 2PA in a thin GaP crystal [33]. There is an advan-tage for using a GaP crystal for the THz generation comparedwith other electrooptic materials such as LiNbO3 and ZnTecrystals: a GaP crystal has much lower absorption coefficientsand shorter cutoff wavelength in the THz domain comparedwith LiNbO3 and ZnTe crystals [34]. Therefore, the output THzpulses can be extended to much higher frequencies. Indeed, asdemonstrated in [35], the usable bandwidth for GaP can be asbroad as 7 THz. In the past, GaP was used to generate THzwaves through optical rectification [35] as well as by usingtwo infrared coherent sources based on noncollinear [36] andcollinear [37] configurations for the DFG. Consistent with ourprediction [17], [18], see also Section II earlier, a conversionefficiency for THz generation as high as 6.5 × 10−5% [38] wasachieved using an Yb-doped fiber amplifier.

Fig. 3. Coherence lengths calculated using (6) are plotted as a function ofoutput wavelength for GaP, ZnTe, and GaSe at the pump wavelength of 790 nm.

The GaP and other materials (i.e., ZnTe, InAs, GaAs, andInP) studied by us in the following all belong to the point groupof 43m. According to our calculation, a (111)-cut GaP crystalis the optimal orientation for optical rectification since it yieldsthe highest effective nonlinear coefficient when the incident an-gle is close to the Brewster angle. As one can see later, we areable to generate relatively high output powers and conversionefficiencies from a 0.45-mm-thick (111) GaP crystal after ge-ometrically minimizing the effect of 2PA. Indeed, broadbandTHz pulses with an output power of 4.4 µW, corresponding toa conversion efficiency of 0.00044%, have been generated byusing a Ti:Sapphire regenerative amplifier with a central wave-length of 790 nm, a pulse width of 180fs, and a repetition rateof 250 kHz. The highest average output power from the regen-erative amplifier is 1 W, which corresponds to energy per pulseof 4 µJ. The pump pulses are focused into the GaP crystal bya convex lens with the focal length of f = 50 mm. The THzoutput powers including those in the following sections are mea-sured by using a calibrated bolometer and calibrated DLATGSpyroelectric energy meter operating at room temperature.

Following the discussions in Section II, the central wave-length of the THz radiation generated by the pump pulses de-scribed earlier is around 160 µm with a bandwidth from 90 to340 µm for the phase-matched optical rectification. In Fig. 3,we have plotted the calculated coherence lengths for GaP at thepump wavelength of 790 nm. One can see that even though theoptical rectification is not phase matched for a GaP crystal usingthe regenerative amplifier, the coherence lengths are quite longwithin the theoretical bandwidth of 90–340 µm. Therefore, wecan use the regenerative amplifier to efficiently generate broad-band THz radiation in a thin GaP wafer. Totally, we have mea-sured six GaP crystals with the orientations of (100), (110), and(111) and lengths in the range from 0.35 to 20 mm. Among thesix crystals acquired from different sources, the 0.45-mm-thick(111) GaP wafer produced the highest output power in the THzregion. In order to confirm the mechanism for the THz genera-tion, we have measured the dependence of the THz polarization


Fig. 4. Measurement of polarization of the THz wave as a function of thepump polarization for GaP (both the angles were measured with respect to thep polarization direction).

Fig. 5. Spectra of THz output pulses measured by using a grating on GaP,ZnTe, GaSe, and InN. Dips appearing in the spectra were caused by the absorp-tion of water vapor present in the beam path. NR and R are used to designatenonresonant and resonant excitation conditions.

on the pump polarization, see Fig. 4. Using the three nonzeroelements of the second-order susceptibility tensor, i.e., d14 , d25 ,and d36 , we have calculated the dependence. One can see fromFig. 4 that our data are consistent with the calculated valuesbased on the three elements. The spectrum of the output THzpulses is also measured by using a diffraction grating optimizedwithin the THz region, see Fig. 5. One can see that the centralwavelength of the THz output spectrum measured by us is quiteclose to the calculated value by using (4). On the other hand,the bandwidth is measured to be narrower than the calculatedvalue based on (4). Such a difference is due to the absorption ofthe THz pulses and oscillation of the phase-matching term as afunction of the output wavelength. In the spectrum of the THzpulses, we have observed many dips that are attributed by us tothe absorption of water vapor in the beam path after comparing

Fig. 6. Average THz output power versus average optical pump power foreight electrooptic crystals.

Fig. 7. Transmittance for pump beam (open circles) and THz output power(dots) versus distance between focal point of pump beam and GaP wafer.

the locations of these dips with the resonance frequencies of thewater vapor available from the Hitran database.

We have also measured the dependence of the average THzoutput power on the average power for the pump beam, seeFig. 6. At relatively low levels of the pump power, the depen-dence is close to a square law, which is expected for opticalrectification. However, for the average pump powers of higherthan 650 mW, the dependence of the THz power on the pumppower becomes approximately linear. Therefore, we believe thatthere must have another nonlinear process competing with theoptical rectification.

When the pump beam was focused inside the GaP wafer, theTHz output power was the lowest, see Fig. 7. At the same loca-tion, the transmittance of the pump beam was also the lowest,see Fig. 7. In this case, the 2PA was strongest whereas the THzgeneration was inefficient. However, as the focal point of thepump beam was moving away from the GaP wafer, the THzoutput power went through two maximum values (one on eachside of the wafer). When the diameter of the laser beam inside


TABLE IHIGHEST AVERAGE OUTPUT POWERS (sPT ,a ), CONVERSION EFFICIENCIES

(η), AND CONVERSION EFFICIENCIES NORMALIZED BY THE PEAK PUMP

POWERS (η/Pp ) MEASURED ON THESE ELECTROOPTIC (EO) MATERIALS

the wafer was sufficiently large, the 2PA was dramatically re-duced. However, if the beam diameter was too large, the THzpower generated from the wafer based on optical rectificationwas too low. Following our measurement, the highest averagepower generated from the GaP wafer was 4.4 µW for the p-polarized pump beam with an incident angle near the Brewsterangle, see Table I. The corresponding conversion efficiency wasthen determined to be ∼ 4.4 × 10−4%, which was translatedinto a normalized conversion efficiency of 0.019%/GW. Sucha conversion efficiency is an order of magnitude higher thanthat achieved by using the fiber laser amplifier [38]. Using (12),the conversion efficiency is calculated to be 0.019%, which is afactor of 42 higher than our measured value. Such a differencecan be attributed to the presence of 2PA and absorption of theTHz pulses generated by the optical rectification.

For comparison, we have also studied the THz generationfrom ZnTe. A ZnTe plate used in our experiment has a thicknessof 0.5 mm along the [111] direction. Since the ZnTe crystal be-longs to the same point group as GaP, the THz pulses generatedfrom these two crystals share similar output characteristics. Firstof all, we have measured the dependences of the polarizationand output power for the THz pulses on the pump polarization,see Fig. 8. One can see from Fig. 8 that when the pump beam isp-polarized (i.e., 0 and 180) the THz power reaches the max-imum values. On the other hand, when the polarization anglesfor the pump beam are within the range of 60–110, the outputpowers are quite low. These dependences represent typical be-haviors for the THz generation based on the optical rectificationin zinc blende crystals. We have also measured the dependenceof the output power on the pump power, see Fig. 6. When thepump power is below 800 mW, the power dependence is closeto quadratic. However, above 800 mW, the dependence devi-ates from quadratic. We believe that this deviation originatesfrom the presence of 2PA, which is consistent with the previousresults [39], [40]. At the pump power of 953 mW, the highestoutput power is measured to be 29.7 µW, which is an order ofmagnitude higher than that generated from the GaP crystal, seeTable I. In this case, the incident angle is quite close to the Brew-

Fig. 8. Polarization and output power for THz versus polarization of thepump beam for ZnTe plate (both the angles were measured with respect to thep polarization direction).

ster angle and the pomp beam is p-polarized. The conversionefficiency normalized by the peak pump power is 0.15%/GW,which is higher than the highest value achieved in [13] by twoorders of magnitude. Compared with the spectrum for the GaPcrystal, the output powers generated from the ZnTe crystal arerelatively higher in the range of 150–250 µm (i.e., in the high-frequency end of the spectrum), see Fig. 5. Such differencesmay be attributed to the fact that the ZnTe crystal has muchlonger coherence lengths than GaP in this wavelength range,see Fig. 3.

B. GaSe

Besides the GaP and ZnTe crystals, we have also investi-gated the THz generation from a 145-µm-thick z-cleaved GaSecrystal. GaSe crystals have been used to efficiently generatewidely tunable THz pulses based on the DFG [41], [42]. Sucha crystal was also used to detect THz pulses based on elec-trooptic sampling [43] and THz frequency upconversion [44].Since it belongs to the point group of 62m, its second-ordernonlinear susceptibility tensor has three nonzero elements:d16 = d21 = −d22 = 0. Therefore, the optimal wave propaga-tion direction for the optical rectification is the [001] axis thatis perpendicular to the cleaved surface. The power dependencefor GaSe at the normal incidence is plotted in Fig. 6. One cansee that it is close to a square law in the entire range of the pumppowers. The slight deviation of our data from the quadratic de-pendence is caused by the 2PA [45]. The highest THz outputpower generated from the GaSe crystal is about 5.4 µW forthe pump power of 926 mW. The corresponding conversion ef-ficiency normalized by the peak pump power is 0.028%/GW,which is a factor of about 5 lower than that for the ZnTe crystal,see Table I.

Theoretically, the THz output power is independent of thepump-polarization angle when the pump beam propagates alongthe optic axis of the crystal. However, from our experimentalresult, the THz output power strongly depends on the pump-polarization angle, see Fig. 9. The maximum and minimum THzoutput powers occur when the pump polarization is parallel to


Fig. 9. THz output power is measured versus polarization of the pump beamfor GaSe (dots) (x-axis of the crystal is the reference axis for the measuredpolarization angles). Solid curve: nonlinear least-square fitting to the dots using(16) whereby d16/d22 and d21/d22 are the two adjustable parameters.

x- and y-axes of the crystal, respectively. As mentioned earlier,for a GaSe crystal, the second-order nonlinear susceptibility ten-sor has three nonzero matrix elements. Therefore, the nonlinearpolarization oscillating at the THz frequency is given by

Px = 4d16ExEy ; Py = 2d21E2x + 2d22E

2y . (15)

Substituting Ex = E0 cos θp and Ey = E0 sin θp into (15),where θp is the angle of the pump polarization formed withthe x-axis of the crystal and E0 is the amplitude of the pumpelectric field, one obtains the expressions for the square of thenonlinear polarization and the polarization angle of the THzwave formed with the x-axis

P 2T = P 2

x + P 2y

= 2d222E

40

2(

d16

d22

)2

sin2 (2θp) +(

d21

d22

)sin2 (2θp)

+2(

d21

d22

)2

cos4 θp + 2 sin4 θp

(16)

θT = tan−1[(d21/d22) cos2 θp + sin2 θp

(d16/d22) sin (2θp)

]. (17)

When the Kleinman’s symmetry condition is valid and for thepoint group of 62m, d21/d22 = −1 and d16/d22 = −1, one canthen simply (16) and (17) to

P 2T = 4d2

22E40 ; θT =

3π

2− 2θp (18)

i.e., the THz output power is independent of the pump polariza-tion and for every rotation angle of 180 for the pump polariza-tion, the THz polarization rotates by 360. Unfortunately, ourexperimental result indicates that the THz output power stronglydepends on the pump polarization, see Fig. 9. If we assumed16 = d21 and d21 = −d22 , we can then use (16) to fit our data.

Fig. 10. Polarization of THz beam is measured versus polarization of pumpbeam at normal incidence for GaSe (dots) (x-axis of the crystal is the referenceaxis for the measured polarization angles). Solid curve: theoretical result basedon (17) whereby d21/d22 ≈ −1.36 and d16/d22 ≈ −1.17.

As a result of the nonlinear least-square fit, we have obtained:d16/d22 ≈ −1.17 and d21/d22 ≈ −1.36, i.e., d16 ≈ 0.859d21 .Using these ratios, our data are in a very good agreement withour theoretical dependence, see Fig. 9. The Kleinman’s symme-try condition is valid only when the frequencies of the partici-pating waves are sufficiently above the ionic resonances of thecrystal [20]. When the THz frequencies are below the phononabsorption band, such a condition is no longer valid. The sig-nificant deviation of d21 from −d22 is probably caused by theasymmetric residual strain originating from the crystal growth,which makes the point group of the GaSe crystal significantlydeviate from 62m.

Since the point group for GaSe is different from that forGaP and ZnTe, the polarization at the maximum THz outputpower for the GaSe crystal is measured to be perpendicular tothe pump polarization. Besides the orthogonal polarizations, thedependence of the THz polarization on the pump polarization issimilar to that for the two zinc blende type crystals, see Fig. 10.One can see that when the pump polarization is rotated by 180

(clockwise or counterclockwise), the THz polarization angle ischanged by 360 (counterclockwise or clockwise). The theoret-ical polarization dependence based on the optical rectification isalso plotted in Fig. 10 by using (17) whereby d16/d22 ≈ −1.17and d21/d22 ≈ −1.36. One can see from Fig. 10 that althoughthe values of d16/d22 and d21/d22 strongly affect the THz outputpowers they have only slightly modified the polarization anglesof the THz output beam. Nevertheless, our data can be betterfitted by using (17) with the optimal values of d16/d22 ≈ −1.17and d21/d22 ≈ −1.36 than using the second expression in (18),especially for the pump polarization angles within 0–90. Fromthe following section, one can see that such polarization depen-dence is one of the signatures for optical rectification. Whenphotoconductive effect becomes important, the direction of theTHz polarization swings back and forth around the p polariza-tion direction as the pump polarization changes.


IV. RESONANCE-ENHANCED THZ CONVERSION

In this section, we summarize our recent results on the ef-ficient generation of THz pulses from InN, InAs, GaAs, andInP crystals. Since our pump photon energy is higher than thebandgap of each of the four materials, the output powers aregreatly enhanced by utilizing the resonant second-order nonlin-earities of these materials.

A. InN Thin Films

Consider the InN films. Highly efficient conversion from ul-trafast optical pulses to the THz counterparts has been achievedfrom wurtzite InN thin films. The average THz output poweras high as 0.931 µW has been obtained by us [46]. Recently,InN films were used for generating THz radiation by usingultrafast laser pulses [47], [48]. The mechanism for the THzgeneration was assigned to either transient photocurrent [47] orphoto-Dember effect [48].

We used the same Ti:sapphire regenerative amplifier de-scribed in Section III as a pump source. After passing througha half-wave plate, the amplifier beam was focused by a positivelens (f ≈ 50 mm). Each InN sample was sequentially placed inthe beam path with the InN side being illuminated by the ampli-fier beam at a location of 5 mm away from the focal point eitherbefore or after it (the beam diameter is 400 µm), see the insetof Fig. 11(a). The THz beam generated in the forward direc-tion was then collected by a parabolic mirror and subsequentlydetected by an accurately calibrated bolometer and pyroelectricenergy meter. Polyethylene and germanium filters were insertedin the front of each detector to block the unconverted pumpbeam.

Nine InN films were grown on (0001) sapphire substrates,each of which had a 4 µm semiinsulating GaN buffer layergrown by Vecco Gen 930 molecular beam epitaxy system at490–510 C, see Table II. X-ray diffraction studies confirmedthat these InN films all had a wurtzite structure with their c-axis perpendicular to the substrate surface [49]. Although theseInN films were not intentionally doped, they all had quite highelectron densities, see Table II. The bandgaps of these filmswere measured by us to be about 0.61 eV [50]. For each InNfilm sample, we measured the THz output powers at differentpump powers. Among all the samples, the highest output powerachieved in our experiment was 0.931 µW for an average pumppower of 1 W, from the 700-nm-thick InN film, i.e., sample 3 inTable II. Moreover, the THz powers from all the InN films wereindependent of the azimuthal angle, similar to [47]. However,the THz output power strongly depended on the polarizationand incident angle of the pump beam, see Fig. 11(a) and (b).The maximum output power occurred at θi ≈ 60 and for a p-polarized pump beam (i.e., ϕ ≈ 0, where ϕ is the angle ofthe pump polarization formed with respect to the plane of in-cidence), see the inset in Fig. 11(a). In such a case, the THzbeam was measured to p-polarized using a wire-grid polarizer.When the pump polarization was s-polarized (i.e., ϕ ≈ 90),the output power was dramatically reduced from the maximumvalue. The ratio between the maximum and the minimum out-put powers was determined to be 6.4. Such a large ratio cannot

Fig. 11. Normalized output power (dots) and square of the effective nonlinearcoefficient (solid curves) are plotted as a function of (a) polarization angle forthe pump beam and (b) incident angle of the pump beam. All the results wereobtained on sample 3 at a pump power of 1 W. Inset: configuration for THzgeneration from an InN film.

TABLE IIDESCRIPTION OF INN SAMPLES INVESTIGATED IN OUR EXPERIMENT

be induced by the polarization dependence of the overlap be-tween the photocarrier distribution and high electric-field regionobserved previously [51].

The output power is measured to be quadratically dependenton the pump power when the pump power was less than 80 mW,


Fig. 12. Highest average output power for the THz radiation is plotted as afunction of InN film thickness. Broken curve corresponds to fitting based on aquadratic dependence; solid curve represents nonlinear least-square fit to ourdata after the absorption for the pump beam is taken into consideration.

see Fig. 6. For higher pump powers, however, the dependenceapproached linear. Since the photon energy of the pump beamwas above the bandgap of the InN films, the absorption of thepump beam by the film can be quite high [52]. Therefore, at rel-atively higher pump powers, the temperature of the film withinthe pumping area was significantly increased, which may causethe absorption coefficient to be increased [53]. In addition, onecan see from Fig. 12 that the THz output powers from samples3 and 5–8 form a quadratic dependence on the film thickness.However, for samples 1 and 4, the output powers were muchless than those from sample 3, probably due to the much higherFCA losses for the THz beams.

As mentioned earlier, for a wurtzite crystal, the THz out-put power is independent of the azimuthal angle of the crystal.Therefore, unlike a zinc blende crystal, the azimuthal depen-dence alone cannot be used to identify the mechanism for theTHz generation in the InN films. In order to pinpoint the mech-anism for the THz generation, we have taken one step further tomeasure the dependence of the THz polarization on the pumppolarization. One can see from Fig. 13 that the THz polariza-tion strongly depends on the pump polarization. Such a be-havior cannot be caused by the photocurrent surge since theTHz polarization due to such a mechanism is independent ofthe pump polarization. In addition, such a dependence is differ-ent from the theoretical curve based on the optical rectificationin an ideal wurtzite crystal, see Fig. 13. Moreover, the depen-dences measured on the nine samples are not consistent withone another. Fig. 13 just illustrates one of the most commonones. The significant deviation of the measured dependencefrom our theoretical curve shown in Fig. 13 is currently underinvestigation.

In order to explain the dependences observed in Fig. 11, wehave expressed the square of the effective nonlinear coefficientusing the equation: d2

eff = (dx cos θt + dz sin θt)2 + d2

y , where

Fig. 13. Typical THz polarization versus pump polarization measured on InNfilms (dots) (both the angles were measured with respect to the p polarizationdirection). Solid curve corresponds to our theoretical dependence.

dx, dy , and dz are

dx = 2d31 cos2 ϕ cos θt sin θt

dy = 2d31 cos ϕ sin ϕ sin θt

dz = d31 cos2 ϕ cos2 θt + d31 sin2 ϕ + d33 cos2 ϕ sin2 θt .(19)

In (19), θt is the incident angle for the pump beam inside theInN film and the x- and y-axes are chosen to be parallel toand perpendicular to the plane of incidence, respectively. InFig. 11(a), d2

eff is plotted versus ϕ for θi = 60 by assuming thatd31 = d15 and d33 = − 2d15 [54]. Although the first relationis valid for a lossless medium [20], [27], we assume that itcan be still used for the THz generation. The second one isderived from bond additivity [55]. Under these assumptions, d2

effclosely matches our data, see Fig. 11(a). The deviation of ourtheoretical result from the data in Fig. 11(a) could be caused bythe fact the relations among the three nonzero elements of thesecond-order nonlinear susceptibility tensor, imposed earlier,are approximately valid. Similarly, the dependence of d2

eff onθi for ϕ = 0 is in an excellent agreement with our data forθi < 60, see Fig. 11(b). Above 60, however, since the InNsample with the dimension of ∼5 mm × 5 mm acts as anaperture, the output power measured by us starts to decrease.

Based on (10), the average output power is shown to be

PT ,a ≈ 0.6038η0d2eff Pp,aPp [1 − exp (−αL)]2

c2npgn2pτ

2p Apα2 (20)

where Pp and Pp,a are the peak and average powers and α isthe absorption coefficient for the pump beam. One can see from(20) that the output power quadratically depends on the thick-ness of the film, which is consistent to our experimental results,see Fig. 12. Since the photon energy at the pump wavelength iswell above the bandgap of the InN films, the absorption of thepump beam can be large, especially for thick films. Using α as


TABLE IIIELEMENTS OF SECOND-ORDER NONLINEAR SUSCEPTIBILITY TENSORS

ARE DETERMINED FOLLOWING OUR MEASUREMENTS MADE ON

INN, INAS, GAAS, AND INP

an adjustable parameter, we have achieved the nonlinear least-square fitting of our data by using (20) when α ≈ 4000 cm−1 .As a result, our theory is in a better agreement with the dataafter including the absorption of the pump beam, see Fig. 12.Using PT ,a ≈ 13.4 nW for Pp,a ≈ 50 mW, L ≈ 0.7 µm, τp ≈180 fs, Ap ≈ 0.126 mm2 , np ≈ npg ≈ 3, and α ≈ 4000 cm−1 ,we have estimated d15 to be 7.12 nm/V using (20), seeTable III. This value is three orders of magnitude higher than thenonresonant value [56]. Such a large value originates from theresonant enhancement of the optical rectification. Indeed, suchan enhancement was previously observed in a GaAs crystal [57].Similar to [57] and [58], the generations of electron-hole pairsin the InN films have dramatically enhanced the nonlinear co-efficients. Based on our measurement made on sample 3, wehave determined the highest value for the conversion efficiencynormalized by the square of the film thickness [see (11)] to be190% mm−2 . This resonant value is four orders of magnitudehigher than that for the ZnTe crystal (i.e., 0.012% mm−2), seeSection III given earlier.

B. InAs

THz radiation from InAs has been demonstrated to be quiteefficient [59]–[61]. However, the mechanism for the THz gen-eration from this material has not been settled yet. On one hand,the THz output power was found to periodically depend on theazimuthal angle of InAs, which indicates that the THz gener-ated in InAs originated from optical rectification [59], [61]–[63].Since the pump photon energy is much higher than the bandgapof InAs, these second-order nonlinear coefficients are reso-nantly enhanced due to the presence of the electronic tran-sitions [57], [58]. Moreover, due to the presence of a largebuilt-in electric field in this material [64], [65], the electric-field-induced surface second-order nonlinearities were also consid-ered to be the mechanism for the THz generation [66]–[69].On the other hand, the THz output power from InAs was foundto strongly depend on the type of dopants, doping level, andapplied electric and magnetic fields [57]–[59], [61]–[66], [70],which suggested that the broadband THz radiation generatedfrom InAs be induced by photocurrent surge. However, it wasunclear whether the photocurrent surge was caused by the driftof the carriers under the surface built-in field or photo-Dembereffect [59], [62], [63], [70].

Since the electric field of the broadband THz pulses is drivenby the polarization induced by the pump pulses at the THzfrequencies, the key for fully understanding the mechanisms forthe THz generation in InAs is the polarization behaviors of the

Fig. 14. Spectra of THz output beams measured on InAs, GaAs, and InPcrystals.

THz pulses, which have not been carefully investigated in thepast. Furthermore, the absolute output powers produced fromInAs have rarely been measured in the past.

In the following, we summarize our results obtained on anInAs crystal [71]. The InAs sample used in our experimentwas a 0.5-mm-thick p-type (111) wafer with a hole density of3 × 1017 cm−3 . The pump source was a Ti:sapphire regenera-tive amplifier with the output wavelength of 790 nm, the pulsewidth of 180 fs, and the repetition rate of 250 kHz. A convex lenswith a focal length of 50 mm was used to focus the pump beamon the InAs sample at the incident angle of θ ∼ 75. The InAssample was placed at a location away from the focal point eitherupstream or downstream by 5 mm with respect to the propaga-tion direction of the pump beam. The beam radius at the samplesurface was about 200 µm for the normal incidence. The THzsignal was collected by a parabolic mirror and detected by a cal-ibrated bolometer and pyroelectric energy meter in a reflectiongeometry. A polarizer was used to investigate the polarizationcharacteristics of the output THz pulses. Fig. 14 illustrates atypical spectrum of the THz output from the InAs sample. Onecan see from Fig. 14 that the THz output is broadband, coveringthe wavelength range of 200–1200 µm.

THz output power underwent through three cycles of the os-cillation as a function of azimuthal angle (α) within 360, seeFig. 15(a). Such a behavior is similar to some of the previ-ous results [57], [62], [69]. The maximum and minimum THzoutput powers for p-polarization corresponded to the minimumand maximum values for the s-polarization, respectively. More-over, the maximum output power for the s-polarized pump beamwas much lower than that for the p-polarized pump beam. Theoutput THz power for the p-polarized pump beam reached amaximum value (that for the s-polarized pump beam reaches aminimum value) only when the projections of the pump prop-agation direction and one of the principal crystal axes onto the(111) plane were opposite to each other (i.e., α = 0). Due tothe crystal symmetry, for every 120, the output power reached


Fig. 15. Azimuthal-angle dependences of (a) THz output power and (b) THzpolarization angle relative to p polarization direction for θ ≈ 75 and pumppower of 926 mW for InAs. Solid curves correspond to fitting to data by using(22).

a maximum or minimum value again. The difference betweenthe output powers for the two pump polarizations is primarilycaused by the high reflection loss for the s-polarized pump beamat the air/InAs interface. Indeed, according to [72], the refractiveindex of InAs at 790 nm is around 3.74. Therefore, the reflec-tion losses for the pump beam under our experimental conditionswere about 0% and 78% for the p- and s-polarized pump beams,respectively. The highest output power was measured to be 56.5µW at an average pump power of 926 mW, corresponding to aconversion efficiency of about 0.0061%. This number is trans-lated into a normalized conversion efficiency of 0.30%/GW, seeTable I, which is higher than that achieved in [13] by a factor of∼200. The dependence of the THz output power on the pumppower was measured to be nearly quadratic for the pump powersof lower than 136 mW, see Fig. 6. Above such a pump power,however, the dependence significantly deviates from the squarelaw.

The directions of the THz polarizations for the p- ands-polarized pump beams were found to swing around the ppolarization direction back and forth as a function of azimuthalangle, see Fig. 15(b). Moreover, their directions were alwaysopposite to each other. The maximum angles (β) for the polar-

Fig. 16. Pump-polarization dependences of (a) THz output power and (b) THzpolarization angle for θ ≈ 75 and pump power of 926 mW for InAs (both theangles were measured with respect to the p polarization direction). Solid curvesare theoretical curves based on (22) and (23).

izations relative to the p polarization direction were measuredto be 32.2 and 13.5 for the p-polarized and s-polarized pumpbeams, respectively. Similar to the output power, the THz po-larization for each pump polarization completes three periodsof the oscillation with changing the azimuthal angle by 360.At the azimuthal angle of α = 0, the THz output power andpolarization as a function of pump polarization were also mea-sured, see Fig. 16(a) and (b). For every 360 rotation, the THzpolarization oscillated back and forth around the p polarizationdirection for two periods with a maximum angle of 13. On theother hand, the THz output power reached a maximum value forthe p-polarized pump beam.

According to Fig. 15(a), optical rectification is evidenced byan oscillation period of 120. However, since InAs has the samepoint group as GaP and ZnTe, the polarization of the THz radia-tion generated by the optical rectification should monotonicallychange by 360 for every 120 of the azimuthal angle or 180 ofthe pump polarization angle as we have demonstrated in SectionIII earlier. From Fig. 15(b) and Fig. 16(b), one can see that suchan expected behavior contradicted with our experimental result.In order to explain our experimental result, we consider thepossible contribution of the photoconductive effect to the THz


generation. However, since the THz radiation measured in ourexperiment is highly polarized, the THz electric field caused byphoto-Dember effect due to the diffusion of the photogeneratedcarriers in the lateral directions has been ruled out by us. Basedon our estimates of the densities of the photogenerated carriers,the THz electric field caused by photo-Dember effect due to thediffusion of the carriers in the direction opposite to the surfacenormal would be proportional to the pump intensity accordingto [73]. This is inconsistent with what we have observed onour InAs sample, see next. Therefore, the photocurrent surgeis primarily induced by the drift of the carriers under the sur-face built-in electric field. Accordingly, the p and s componentsof the total polarizations oscillating at THz frequencies can bewritten as

PP = χ(2)eff ,P |E|2 + PJ sin(θ)

PS = χ(2)eff ,S |E|2 (21)

and the polarization angle β and the magnitude of the polariza-tion can be determined by

tan(β) = PS /PP ; P =√

P 2P + P 2

S (22)

where χ(2)eff ,P and χ

(2)eff ,S are the effective second-order nonlin-

ear coefficients for producing the THz p and s polarizations,respectively. They are a function of incident angle, azimuthalangle, and pump polarization angle, which can be derived fromthe second-order susceptibility tensor for InAs [63]. In (21),PJ = ∂J/∂t is the polarization induced by the photocurrentsurge along the surface normal. In order to directly compare thecontributions made by the optical rectification and photocur-rent surge, a pseudo-nonlinear coefficient is introduced by ussuch that PJ = κ |E|2 in (21). As a result, (22) can be used toachieve the nonlinear least-square fitting to the data presented inFig. 15(a) and (b): θ ≈ 76.8, κp ≈ 2.94χ14 , and κs ≈ 7.60χ14for the p- and s-polarized pump beams, respectively. One cansee that this value of θ is close to the incident angle directlymeasured by us. Based on the fitting, the contribution of thephotocurrent surge to the THz electric field is about 76% and46% for the s-polarized and p-polarized pump waves. One cansee that the pseudo-nonlinear coefficient for the p-polarizedpump is a factor of 2.59 smaller than that for the s-polarizedpump. This is due to the different degrees of the screening of thebuilt-in electric field by the photogenerated carriers for the twopolarizations. Indeed, the internal s-polarized pump intensity isestimated to be about 22% of the p-polarized pump intensityunder our experimental conditions.

Assuming that the polarization induced by the photocurrentsurge is proportional to the surface built-in electric field [74],an empirical model can be proposed to reflect the screening ofthe built-in field by the photogenerated carriers:

PJ = PJ,0 [1 − exp (−I/Isat)] (23)

where I = Pave cos θ/πw2

0 is the average pump intensity withPave and w0 the average pump power and pump beam radius,respectively, PJ,0 is the polarization induced by the surface built-in field without the screening effect and Isat is the saturation

Fig. 17. Effective and pseudo nonlinear coefficients are plotted as a functionof normalized pump intensity for InAs. For the highest pump power of 926 mWused in our experiment, I/Isat ≈ 3.731.

intensity. Using the values of κp and κs determined through thefitting, PJ,0 ≈ 3.00χ14 |E|2 and Is ≈ 51.1 W/cm2 . One cansee from Fig. 17 that the photocurrent surge is dominant onlyat low pump intensities. However, at sufficiently high pumpintensities, the polarization induced by the photocurrent surgebecomes negligible due to the screening of the built-in field bythe photogenerated carriers, causing the steep reduction of κwith increasing the pump intensity, see Fig. 17. Therefore, it isobvious that due to the resonant enhancement of the second-order nonlinearities [57], [58] the optical rectification becomesthe dominant mechanism for the THz generation in InAs un-der sufficiently high pump intensities. Indeed, based on (20),the second-order nonlinear coefficient for InAs χ14 can be es-timated to be as high as 130 nm/V, see Table III. This value ishigher than the nonresonant value of InAs by three orders ofmagnitude.

Using (22) and (23), the dependences of the THz output powerand polarization on the pump polarization have been determined,see in Fig. 16(a) and (b). One can see that our calculations areconsistent with our experimental results. Therefore, our empir-ical model, i.e., (23), is valid for describing the polarizationgenerated by the photocurrent surge under the built-in electricfield screened by the photogenerated carriers.

Although effective second-order nonlinearities can originatefrom third-order nonlinearities in a dc surface electric field [68],our calculation based on [75] shows that the THz polarization di-rection should be along the p polarization direction within±0.5

regardless of the pump polarization. Such a behavior is com-pletely different from our experimental result, see Fig. 16(b).

C. GaAs and InP

Among different electrooptic materials, GaAs has a large ef-fective second-order nonlinear coefficient below its bandgap.Above the bandgap, the nonlinear coefficient should be res-onantly enhanced. Indeed, it was demonstrated in the past[57] that the enhancement can be as high as two orders of


magnitude. In the following, we demonstrate that the polariza-tion characteristics of the THz pulses can be used to determinethe contributions made by the optical rectification and pho-tocurrent surge to the THz generation from GaAs. We havealso measured the THz output powers. Based on the contribu-tion made by the optical rectification, we have determined thesecond-order nonlinear coefficient and confirmed the resonantenhancement on the nonlinear coefficient. For comparison, wehave also investigated the THz generation from an InP crystal.Since both of the GaAs and InP have the same point group asInAs, the analysis made by us in Section IV-B earlier can bedirectly applied to these two crystals.

Our GaAs sample is a semiinsulating 360-µm-thick (111)GaAs wafer. It has an extremely low carrier concentration of8.9 × 106 cm−3 and a Hall mobility of 6859 cm2 /(V · s). Onthe other hand, our InP sample is a 337-µm-thick (111) semiin-sulating InP doped by Fe. This sample has a carrier concentrationof 6.0 × 107 cm−3 and a Hall mobility of 1342 cm2/(V · s). Wehave first measured the dependences of the THz output powerson the pump powers, see Fig. 6. They both significantly deviatefrom the square law. The highest output powers generated fromthe GaAs and InP crystals are both measured to be 1.2 µW forthe pump powers of 964 and 700 mW, respectively, with thecorresponding conversion efficiencies listed in Table I. We havealso measured the dependences of the THz output power on thepump polarization, see Fig. 18(a). One can see that the curvesfor these two materials resemble each other. However, it is ob-vious that the minimum output powers for InP are significantlyhigher than those for GaAs. We believe that such differencesare due to the fact that the contribution originating from pho-tocurrent surge to the THz generation is significantly higher forInP. In fact, according to Fig. 8, the minimum output powersshould be close to zero when the contribution from the pho-tocurrent surge is negligible. In such a case, one would expectthat the THz polarization is much less dependent on the pumppolarization for InP. This is indeed confirmed by our measure-ment, see Fig. 18(b). In terms of the spectra for the THz outputpulses, GaAs provides us with much higher output powers thanInP for the wavelengths shorter than 500 µm, see Fig. 14. InAsproduces much higher THz output powers than GaAs and InPalmost within the entire wavelength range.

One can also determine the amount of the contribution fromthe optical rectification to the THz generation from the mea-surement of THz output power as a function of incident angle,see Fig. 19. The dependences for the optical rectification andphotocurrent surge are completely different from each other.For GaAs, the dominant mechanism is the optical rectification.On the other hand, for InP the photocurrent surge is the primarymechanism for the THz generation. Therefore, based on Fig. 19,the highest output powers generated from GaAs and InP due tothe optical rectification are determined to be 432 and 14.5 nW,respectively. Based on (20), we have estimated the second-ordernonlinear coefficients (d14) to be 15.8 and 8.78 nm/V for GaAsand InP, respectively, see Table III. These values are two ordersof magnitude higher than the respective nonresonant values,similar to the result obtained for GaAs in [57].

Fig. 18. (a) THz output power and (b) THz polarization versus pump polar-ization for GaAs and InP (both the angles were measured with respect to the ppolarization direction). Incident angles are set to those near the correspondingBrewster angles for producing the maximum THz output powers, see Fig. 19.

Fig. 19. THz output power versus incident angle for GaAs and InP. Pumppolarization angles are set to the values for producing the maximum THz outputpowers.


Fig. 20. THz output power versus pump power for InP. Dots: the output powerof the regenerative amplifier is optimized; squares: the THz output power isreduced by adjusting the ejection delay and phase for the regenerative amplifier.

We have also observed a unique power dependence on theInP crystal, see Fig. 20. Indeed, when the output power of theregenerative amplifier is optimized (its pulse width is ∼180 fs),the THz output power is significantly reduced as the pump poweris increased from 250 to 431 mW. However, after adjustingthe ejection delay and phase of the regenerative amplifier (thecorresponding output power is reduced and the pulse width isslightly shorter than 180 fs), such a peculiar behavior has moreor less disappeared. Consequently, the THz output power isdramatically increased. For example, at the pump power of 431mW, the THz output power is increased from 214 to 576 nW. Ourinvestigation indicates that such a unique power dependence iscaused by the competition between the drift and diffusion ofthe photogenerated carriers. At relatively low pump intensities,the photocurrent surge is primarily induced by the drift of thecarriers under the built-in surface field that is present in our InPsample. However, as the pump intensity is increased, the built-insurface field is screened by the drifted carriers, and therefore,the photo-Dember effect becomes the dominant mechanism forthe THz generation. The drift of the carriers under the built-insurface field is more efficient for the THz generation than thephoto-Dember effect. Indeed, after we have applied an electricfield with its direction being parallel to the sample surface, theshoulder appearing in the output power vs. the pump power inFig. 20 has disappeared. The highest output power achieved byus is 33 µW for an applied electric field of 6.13 kV/cm. Undersuch a field, the output power from the InP sample is in the sameorder of magnitude as that from the InAs and ZnTe samples, seeTable I.

V. THZ GENERATION FROM Si

Si is attractive for the THz generation since the absorptioncoefficient is much lower than all the semiconductor materialsstudied earlier, especially at the relatively high frequencies. Inthe past, Si p-i-n diode was used for THz generation [76]. Whenthe diode was illuminated by 70 fs laser pulses at 625 nm, the

Fig. 21. Experimental setup for THz generation from Si on SiO2 . F1 :polyethylene filter; F2 : Ge filter.

output THz radiation peaked around 0.2–0.3 THz. In addition,there was a strong saturation of the THz electric field as the biasacross the diode (resulting in a surface-normal electric field) wasincreased. However, the absolute output THz power and polar-ization were not measured. Instead, a temporal profile of theTHz electric field was measured by using a radiation-damagedSi-on-sapphire dipole antenna with a temporal resolution of0.5 ps limiting the detectable bandwidth.

In the following, we demonstrate [77] that a thin Si film onSiO2 can be used for the efficient generation of broadband THzpulses. Our result is quite different from the previous one [76].Specifically, the photocurrent induced by the laser pulses flowswithin the plane of the Si thin film. The THz output powerreached the maximum value at a much higher frequency (i.e.,1.25 THz or 240 µm), which was measured by us directly.Moreover, the THz output frequencies were further extendedto as high as 4 THz (75 µm). Furthermore, with a relativelylow electric field applied to the Si film (i.e., 233 V/cm), theTHz output power was increased to 0.89 µW. Based on themeasurements of the THz polarizations, we have determinedthe mechanisms for the THz generation.

We have used the same pump source as describe earlier. Afterpassing through a half-wave plate and a positive lens (f =50 mm), the pump beam illuminates the Si-on-SiO2 emitter atabout 3 cm off the focal point of the beam with an incident angleof 60. The THz radiation was collected along the direction ofthe surface normal for the Si film by using a parabolic mirrorand detected by a calibrated bolometer and pyroelectric powermeter, see Fig. 21.

The Si-on-SiO2 sample consists of a 340-nm-thick uninten-tionally doped p-type Si film on the top of 1 µm SiO2 on a(100) Si substrate. The Si film has a resistivity of 18 Ω·cm (thehole concentration of 7.7 × 1014 cm−3). The dimension of thefilm cross section is 10 mm × 6 mm. At first the Si film wasstudied without any electrodes fabricated on it. Two stripes ofthe electrodes separated by 3 mm were then attached to the filmsurface along the two long sides, see Fig. 21.

The maximum THz radiation was found to be along thesurface normal direction of the Si film. The spectrum of theTHz output was measured when the Si film was not biased,see Fig. 22. The peak of the THz power occurred at 240 µm(1.25 THz) whereas the output powers were measurable in therange from 75 (4 THz) to 400 µm (0.75 THz). Compared with


Fig. 22. Spectrum of THz radiation from Si film on SiO2 .

Fig. 23. THz output power versus pump polarization for Si film on SiO2 .

the spectra for all other materials studied earlier except for GaSe,the THz spectrum produced by Si on SiO2 has a much narrowline width. The power dependence of the THz radiation was alsomeasured, see Fig. 6, which corresponds to a linear dependence.The highest output power measured on the unbiased Si film was0.32 µW for an average pump power of 1 W, see Table I. Thedependence of the THz output power on the pump polarizationwas measured, see Fig. 23. One can see that the THz powerreaches a maximum value for the p-polarized pump. Such alarge difference between the THz output powers for the twoperpendicular polarizations is primarily caused by the differentFresnel reflectivities at the Brewster angle. The THz polariza-tion was also measured by using a wired-grid polarizer. TheTHz radiation generated from the unbiased Si film was found tobe unpolarized. Moreover, the THz output power was measuredto reach the maximum value along the surface normal insteadof the reflection direction for the pump beam. These behaviorsare completely different from those obtained on the electroop-tic materials summarized earlier. Upon our detailed analysis,we conclude that the mechanism of the THz generation in theunbiased Si film was photo-Dember effect.

When the Si film was biased (resulting in an in-plane electricfield), the THz output power was measured as a function of

Fig. 24. THz output power versus bias for different pump powers for Si filmon SiO2 . Solid curves correspond to quadratic fitting.

bias at different pump powers, see Fig. 24. One can see that thedependences were quadratic except for the pump powers of 100and 200 mW. The highest average output power was increasedto 0.894 µW for an average pump power of 1 W at a bias of 70 V(an electric field of 233 V/cm), see Table I. Such an output powercorresponds to an enhancement factor of 4.7 over the unbiasedfilm. However, for the pump powers of 100 and 200 mW, thedependences started to deviate from quadratic for the biases ofhigher than 60 V. This is caused by the electric field induced bythe accumulation of the electrons and holes, which is oppositeto the external electric field. Under the external electric field,the THz output beam was linearly polarized with its polarizationdirection being measured to be parallel to the direction of theapplied electric field. Therefore, the mechanism for the THzgeneration is assigned by us to photocurrent surge when anexternal electric field is present in the Si film. We believe thatthrough a further optimization the THz output power can beincreased to several milliwatts.

VI. CONCLUDING REMARKS

In conclusion, we have given a comprehensive review overour most recent results on the efficient generation of the broad-band THz pulses in a class of semiconductor materials. Theyare generated by using a subpicosecond regenerative amplifierat the output wavelength of 790 nm. The highest average poweris measured to be about 57 µW from an InAs crystal. This istranslated into a conversion efficiency of 0.3% per GW of thepeak pump power. We have demonstrated that the polarizationcharacteristics for the THz output beam can be used to preciselydetermine the contributions originating from the mechanismsfor the THz generation. When the photon energy is higher thanthe bandgap of the material, its second-order nonlinear coef-ficient can be enhanced by two or three orders of magnitude.Consequently, the corresponding output power is dramaticallyincreased. We have also demonstrated that the spectra of theTHz output pulses produced from these materials are quite dif-ferent from one another. These broadband THz pulses havepotential applications in chemical detections, THz imaging, andinvestigations of nonlinear interactions between ultrashort THz


pulses and media. For example, for a pump power of 100 kW at300 µm, our rough estimate indicates that conversion efficiencyas high as several percents may be feasible for achieving THzsecond-harmonic generation.

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[77] X. Mu, Y. J. Ding, and Y. B. Zotova, “Silicon thin film on SiO2 : An efficientbroadband terahertz generator,” in Proc. LEOS 2007, ThF3, Orlando, FL,Oct. 21–25.

Xiaodong Mu received the B.S., M.S., and Ph.D. de-grees from Shandong University, Shandong, China,in 1989, 1992, and 1995, respectively.

He was an Associate Professor of crystal materialsat Shandong University during 1995–1998, a Post-doctoral Fellow at Bowling Green State University,Bowling Green, OH, during 1998–2000, and at theUniversity of Arkansas, Fayetteville, during 2000–2002. Since 2003, he has been a Research Associatein the Department of Electrical and Computer En-gineering, Lehigh University, Bethlehem, PA. He is

the author or coauthor of more than 70 published refereed journal articles innonlinear optical effects and devices, terahertz (THz) generation, and charac-terizations of nanostructures and nanodevices. His current research interestsinclude THz generation, applications, and systems, nonlinear optical devices,and short-wavelength solid-state lasers.

Ioulia B. Zotova received the B.S. degree from Russian Mendeleev Universityof Chemical Technology, Moscow, Russia, in 1997, the M.S. degree from Bowl-ing Green State University, Bowling Green, OH, in 1999, and the Ph.D. degreefrom the University of Arkansas, Fayetteville, in 2002.

Since 2003, she has been working at ArkLight, Center Valley, PA. Her cur-rent research interests include terahertz (THz) devices and spectrometers anddetections of biological and chemical agents.

Yujie J. Ding (M’04–SM’05) received the B.S. de-gree from Jilin University, Changchun, China, in1984, the M.S.E.E. degree from Purdue University,West Lafayette, IN, in 1987, and the Ph.D. degreefrom Johns Hopkins University, Baltimore, MD, in1990.

During 1990–1992, he was a Postdoctoral Fellow,and later an Associate Research Scientist at JohnsHopkins University. During 1992–1999, he was anAssistant, and then, an Associate Professor of physicsat Bowling Green State University, Bowling Green,

OH. During 1999–2002, he was an Associate Professor of physics at theUniversity of Arkansas, Fayetteville. In 2002, he joined Lehigh University,Bethlehem, PA, where he is currently a Professor in the Department of Elec-trical and Computer Engineering. He is the author or coauthor of more than110 published refereed journal articles in optoelectronics, nonlinear optics, andquantum electronics. His current research interests include terahertz (THz) gen-eration, amplification and detection, nanostructures and nanodevices, Ramanscattering in nitride heterostructures, and their applications.

Prof. Ding is a fellow of the Optical Society of America. He is the recipientof the Class of 1961 Professorship from Lehigh University, in 2003, and theOutstanding Young Scholar Award from Bowling Green State University, in1996.

Power Scaling on Efficient Generation of Ultrafast Terahertz Pulses

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